Effective Pair-Interactions in Binary Alloys

  • W. Schweika
Part of the NATO ASI Series book series (NSSE, volume 163)


A number of diffuse scattering studies either with x-rays or neutrons have been done in order to study the local or short-range order (SRO) in binary systems, and mostly in alloys. The SRO as an example of a generalized susceptibility can be related to the pair-interactions between the different atoms [1,2]. The configurational energy may be described by (the lattice gas model or) the Ising model:
$$H = \frac{1}{4}\sum\limits_{{j,i}} {V({{{\vec{r}}}_{i}} - {{{\vec{r}}}_{j}}){{\sigma }_{i}}{{\sigma }_{j}}}$$
where the site occupation is denoted by σ i ±1. The attractive idea of using such pair-interactions is that one expects that they are not only capable of describing the attendant measured SRO configuration but also, perhaps the whole coherent binary phase diagram. But the application of such pair-interactions for the calculation of phase diagrams is restricted, since in real alloys the interactions may not only be pairwise and may also depend on composition and temperature etc. A further problem that the pair-interactions could have been only determined within a mean-field approximation [1,2], has meanwhile been solved by the Inverse Monte Carlo (IMC) method [3]. In the particular case of the Ni . 89 Cr . 11 alloy a remarkable agreement between the numerically exact result of the IMC method and the mean-field solution has been found [4]. However in general, this agreement can not be expected.. But the observation that the range of interaction for a real alloy may extend further than only to nearest and next-nearest neighbor is really a new challenge for the standard tools of statistical mechanics, for the Monte Carlo (MC) and even more for the Cluster Variation method (CVM).


Monte Carlo Direct Monte Carlo Simulation Cluster Variation Method Real Alloy Order Disorder Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Krivoglaz M A Theory of X-Ray and Thermal Neutron Scattering by Real Crystals (Plenum Press, New York) 1969Google Scholar
  2. 2.
    Clapp P C and Moss S C Phys Rev 139A, 844 1966Google Scholar
  3. 3.
    Gerold V Kern J Acta Met 35 No2 393–400 1987CrossRefGoogle Scholar
  4. 4.
    Schweika W and Haubold H-G to be published in Phys Rev B 1988Google Scholar
  5. 5.
    Livet F Preprint to be published 1987Google Scholar
  6. 6.
    Binder K Festkörperprobleme — Adv in Sol Stat Phys 26 Grosse P ed 133–168 1986Google Scholar
  7. 7.
    Gehlen P C and Cohen J B Phys Rev 139A 844 1965ADSCrossRefGoogle Scholar
  8. 8.
    Bieber A Gautier F J Phys Soc Jap 53 No6 2061–2074 1984ADSCrossRefGoogle Scholar
  9. 9.
    Lefebvre S Bley F Bessiere M Fayard M Roth M Cohen J Acta Cryst A36 1–7 1980Google Scholar
  10. 10.
    Epperson J E Fuernrohr P Acta Cryst A39 740–746 1983Google Scholar
  11. 11.
    Klaiber F Schoenfeld B Kostorz G Acta Cryst A43 525–533 1987Google Scholar
  12. 12.
    Chassagne F Thesis Univ Paris VI 1986Google Scholar
  13. 13.
    Wagner W Poerschke R Axmann A and Schwahn D Phys Rev B21 3087 1980ADSGoogle Scholar
  14. 14.
    Jankowski A F Tsakalakos T this conference 1987Google Scholar
  15. 15.
    De Fontaine D and Kikuchi R NBS Publication SP 496,999 1978Google Scholar
  16. 16.
    Carlsson A Phys Rev B35 No10 4858–4864 1987ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • W. Schweika
    • 1
  1. 1.Institut fur Festkörperforschung der Kernforschungsanlage Jülich GmbHJülichFed. Rep. of Germany

Personalised recommendations